. Crystal structure prediction and (Hf, Ta)C1-x vacancy ordered structure
. Phonon dispersion curves of (a) Hf5TaC5, (b) Hf3TaC3, (c) Hf6Ta2C7, (d) Hf2TaC2, (e) Hf4Ta2C5, (f) Hf3Ta3C5, (g) Hf2Ta4C5, and (h) HfTa5C5
. Crystal structures of (a) Hf5TaC5, (b) Hf3TaC3, (c) Hf6Ta2C7, (d) Hf2TaC2, (e) Hf4Ta2C5, (f) Hf3Ta3C5, (g) Hf2Ta4C5, and (h) HfTa5C5 All sharing the rock-salt structure; Black square represents the structural vacancy
. Effect of vacancy on mechanical properties for ternary Hf-Ta-C system
. Density of state (DOS) and partial DOS (PDOS) normalized by per (Hf, Ta)C1-x of (a) Hf5TaC5, (b) Hf3TaC3, (c) Hf6Ta2C7, (d) Hf2TaC2, (e) Hf4Ta2C5, (f) Hf3Ta3C5, (g) Hf2Ta4C5, and (h) HfTa5C5(The Fermi level being set at 0 eV)
Compound | Space group | Lattice constants/nm | Above convex-hull /(eV·atom-1)
| ΔHf/(eV·atom-1)
| CN | x |
---|
Hf5TaC5 | Cm | a=0.567, b=0.976, c=0.929, β=145.1°
| 0 | -0.8925 | 5, 5 | 1/6 | Hf3TaC3 | P-1 | a=0.567, b=0.648, c=0.565
α=89.4°, β=69.6°, γ=91.3°
| 0.0007 | -0.8408 | 5/4, 4 | 1/4 | Hf6Ta2C7 | P-1 | a=0.565, b=0.562, c=0.653
α=90.4°, β=72.4°, γ=99.8°
| 0 | -0.8868 | 6/5, 5 | 1/8 | Hf2TaC2 | P-1 | a=0.566, b=0.554, c=0.560
α=119.4°, β=98.4°, γ=102.4°
| 0.0012 | -0.7842 | 4, 4 | 1/3 | Hf4Ta2C5 | P-1 | a=0.559, b=0.561, c=0.559
α=109.1°, β=100.1°, γ=60.3°
| 0 | -0.8604 | 5, 5 | 1/6 | Hf3Ta3C5 | Cm | a=0.558, b=0.963, c=0.644, β=125.2°
| 0.0009 | -0.8161 | 5, 5 | 1/6 | Hf2Ta4C5 | C2/m | a=0.551, b=0.963, c=0.551, β=71.3°
| 0 | -0.7735 | 5, 5 | 1/6 | HfTa5C5 | Cm | a=0.548, b=0.954, c=0.548, β=109.2°
| 0 | -0.7033 | 5, 5 | 1/6 |
|
Table 1. Space groups, lattice constants, enthalpy above the convex-hull, formation enthalpy (ΔHf), concentration of vacancy (x) and coordination number (CN) of Hf or Ta for ternary (Hf, Ta)C1-x vacancy ordered structures
Compound | C11
/GPa
| C22/GPa
| C33/GPa
| C44/GPa
| C55/GPa
| C66/GPa
| C12/GPa
| C13/GPa
| C23/GPa
| B/GPa
| G/GPa
| E/GPa
| Hv/GPa
| G/B | μ |
---|
Hf5TaC5 | 422.9 | 446.8 | 432.1 | 177.0 | 177.0 | 156.1 | 105.3 | 129.0 | 122.5 | 223.8 | 162.7 | 393.0 | 24.09 | 0.7271 | 0.2074 | Hf3TaC3 | 382.3 | 407.8 | 403.3 | 156.7 | 156.7 | 121.6 | 102.9 | 123.1 | 121.8 | 209.3 | 141.4 | 346.1 | 19.88 | 0.6754 | 0.2244 | Hf6Ta2C7 | 454.5 | 482.0 | 472.3 | 180.9 | 180.9 | 171.3 | 122.2 | 135.9 | 114.0 | 239.1 | 170.6 | 413.4 | 24.23 | 0.7133 | 0.2119 | Hf2TaC2 | 365.7 | 399.7 | 384.9 | 136.2 | 136.2 | 108.5 | 121.0 | 118.9 | 112.0 | 205.7 | 128.8 | 319.8 | 16.85 | 0.6265 | 0.2409 | Hf4Ta2C5 | 443.4 | 423.5 | 441.2 | 175.4 | 175.4 | 160.2 | 122.8 | 135.9 | 140.4 | 233.9 | 162.6 | 395.9 | 22.68 | 0.6949 | 0.2179 | Hf3Ta3C5 | 431.3 | 443.6 | 433.6 | 185.4 | 185.4 | 153.1 | 129.2 | 149.3 | 154.0 | 241.4 | 157.2 | 387.5 | 20.34 | 0.6513 | 0.2325 | Hf2Ta4C5 | 476.5 | 446.7 | 477.6 | 199.4 | 199.4 | 161.1 | 141.9 | 163.7 | 155.6 | 257.9 | 168.3 | 414.6 | 21.34 | 0.6525 | 0.2320 | HfTa5C5 | 491.9 | 473.8 | 484.4 | 209.8 | 209.8 | 171.5 | 149.6 | 165.6 | 166.9 | 268.2 | 175.7 | 432.6 | 22.08 | 0.6551 | 0.2312 |
|
Table 2. Calculated elastic constants (Cij) and mechanical properties-bulk modulus (B), shear modulus (G/), elastic modulus (E), Poisson’s ratio (μ), Vickers hardness (Hv) and Pugh’s ratio (G/B) of (Hf, Ta)C1-x vacancy ordered structures